Interpreting proper orthogonal modes of randomly excited vibration systems

Proper orthogonal modes (POMs) of displacements are interpreted for linear vibration systems under random excitation. Excitations are considered for which the Fourier transform is convergent, meaning that the input must have zero mean, and no sustained sinusoidal component. In such a case, the POMs in undamped discrete linear symmetric systems can represent linear natural modes if the mass distribution is known. POMs in one-dimensional distributed-parameter self-adjoint systems can approximately represent the linear normal modes if the mass distribution is known. Simulation examples are presented. Simulations show that these ideas are also applicable under light modal damping.